Based on PSO cloud computing server points location searching
Chen Hua-sha
Information Technology Center Shanghai International Studies University
Shanghai, china, 13916415603 E-mail: [email protected]
Shen jiajie
Computer center of School of Information Science & Technology
East china normal university Shanghai, china, 18817519704 E-mail: [email protected]
Abstract: Aiming to problem of how to optimize the cloud computing location, an improved PSO algorithm is designed to handle this problem, using the improved PSO algorithm servers location and communication cost can be optimized under cloud computing situation. Though theoretical derivation, the correctness of improved PSO algorithm is proofed. The correctness of theoretical derivation is also verified by the experiment.
Keyword: cloud computing, particle swarm optimization, communication cost
I Introduction
With the development of the cloud computing, and more and more application is upload to the cloud side, however the how to locate the cloud computing server node remain a question to debate.
In the paper, an improved PSO algorithm is presented to handle this problem. Though the theoretical deviation, the correctness of the algorithm is proofed. The correctness of the theoretical deviation is verified by the experiment.
The paper is organized as follow: In second section of paper, the related work will introduced. In the third section of paper improved PSO algorithm will be presented. The experiment and its result will appear in forth section. The fifth section is the result.
II related work
2.1 cloud computing
Cloud computing[1] is hot topic both research and
application development. Many paper discus about this topic[2]-[12], for example some paper are more focus to the
definition of the cloud computing other are application establish and the model. It is true that the cloud computing will become a computer organize form of next generation. The cloud computing also cost vary problem, for example how to find the resource in optimization cost
and how to make the friendly inference the in the cloud situation.
2.2 particle swarm optimization
Standard PSO algorithm is first presented by
Kennedy, Eberhart in 1995[13]. After standard PSO
algorithm, there are a lot of improvement, and several application and case have already been solved by the PSO algorithm.
2.2.1 the function of the standard PSO algorithm The position and velocity of swarm as follow:
)
1
(
)
v
,..,
v
,
v
(
,..,
,
iD i2 i1 D 2 1 in
i
V
x
x
x
X
i i i i
（
）
(1)The optimization value of the particle i is marked as:
）
（
i ini
x
x
x
p
1,
i2,...,
(2) The optimization value of the swarm is marked as:）
（
gi1 gi2 gingi
x
,
x
,..,
x
p
(3)Each particle will change position and velocity the every step based on the follow function:
1 1 2 1 1
)
(
)
(
v
k id k id k id k id k gd k id k id k id k idv
x
x
x
p
c
x
p
c
v
(4)2.2.2 The description of the standard PSO algorithm The step of standard PSO algorithm as follow: Step 1: initialize the swarm include the position and velocity
Step 2: using the PSO algorithm to find the optimization value.
Step 2.1: find the optimization value of each particle(
p
i) and optimization value of swarm(p
ig). International Workshop on Cloud Computing and Information Security (CCIS 2013)Step 2.2: update the position and velocity based on function 4.
Step 2.3: calculate the target function value of each particle.
Step 2.4: if step number bigger than maximum step number or the optimization value is reached go to step 3,else go to step 2.1.
Step 3: Print the optimization value
The improved PSO algorithm have been presented by vary papers[14]-[25], for example how to combine the
PSO algorithm with SVM algorithm with optimization parameters and how to use different kind of improved PSO algorithm to solve vary problems.
III Improved PSO algorithm and algorithm's characters
3.1 The assumption and definition of PSO algorithm Assumption 1: The communication cost is increase with the distance between the nodes.
Assumption 2: One cloud server only can locate in several different place which is close to each other. Assumption 3: The center data base can collect all agents’ data after communicated with all agents, and only after it communicate with all agents.
Assumption 4: One city can have several different server nodes.
Definition 1: the number of server which communicate with center base each city node is called as the communication number.
Definition 2: the city server node which is closest to the center data base is called as closest distance between city i and particle k marked as
)
min(
arg
ij k 2 ijkn
p
sn
(5) ijn
is position of city i node j.p
k is particle k.Definition 3 the variable range of the particle i is called as the particle range i. marked as
RP
i.Note: the particle range should include all the server node of one city.
Definition 4: the distance between the city i server j and the center data base is called as the communication length between the city i server j and the center data base k, marked as: 2 k ij ijk
n
sd
dc
(6) ijn
is the city i server j ,sd
k the center data base k. The minimum the communication length between the city i server j and the center data base is called the minimum communication length between city i and data base k, marked as 2 1min
ij k n j ikn
sd
mdc
(7) ijn
is the city i server j ,sd
k the center data base k. Definition 5: the total communication length is called as the total communication length, marked as
m i n j l k ijk iddc
TD
1 1 1 (8) idTD
is the total distance,dc
ijk is the communicationlength between the city i server j and the center data base k.
The minimum value of total communication length is called as the minimum communication length. marked as
id id
TD
MTD
min
(9)3.2 The description of improved PSO algorithm
The description of improved PSO algorithm as follow:
Step 1: initialize the swarm include the position and velocity.
Step 2: using PSO to find the minimum sum distance of the
Step 2.1: find the optimization value of each particle (
p
i) and optimization value of swarm(p
ig).Step 2.2: update the position and velocity based on function 4.
Step 2.3: check all particle location, and if the particle i outside of region fix it.
Step 2.4: calculate the target function value of each particle.
Step2.5 if the step number is bigger than maximum step number or the optimization value go to step 3,else go
to step 2.1.
Step2.6:search the point which is inside of side which
Step 3: print the result server node
From step 2.1 to step 2.4 , the process of improvement PSO algorithm is as same as the standard PSO algorithm. The main difference between the improvement PSO
3.3 The character of improved PSO algorithm
Theorem 1: if every selected node is closest to the center data base the total communication will become the minimum communication length.
Proof:
If the total communication minimum
communication length, according to the function 9 and function 8:
m i n j l k ijk id idTD
dc
MTD
1 1 1min
min
and because all the
dc
ijk independent with each other,the minimum value of function equal to:
m i n j l k ijk m i n j l k ijkdc
dc
1 1 1 1 1 1min
min
So if and only if all the the communication length between the city i server j and the center data base k is minimum, the optimization value will be reached.
Inference 1: if the improvement PSO can find the close point in every city the minimum total communication length will be found.
Proof:
As the theorem 1 if all the minimum communication length between city i and data base k is reached, the minimum total communication length will be found, so if all the minimum communication length is found by PSO
algorithm, the total communication length will be
minimum total communication length.
Theorem 2: if the particle range is small enough, the total communication length will change a little between different rounds of experiment.
Proof:
If the the particle range is small enough that one sity look like one point comparing with the distance between
the citys is very small and look like a point. So the distance different between the different experiment round will be close.
Inference 2: if the particle range is small enough, the total communication length increase with communication number, it is close to direct ratio.
Proof:
According to the theorem 2, if the particle range is small enough that the different between the experiment round will be very small. So if the communication number is n , it is equal to n time experiment of search n closest city agent point to the center data base.
g w idw g w m i n j l k ijkw m i n j l k g w ijkw idTD
dc
dc
TD
1 1 1 1 1 1 1 1 1 idwTD
is the w round of the total communicationlength,
dc
ijkw is communication length between the city i server j and the center data base k in round w andidg
id
TD
TD
1 ...
The
TD
idg is g round total communication length.So the total length of the communication length is close to the sum of n time of the total length of communication length when communication number is 1.
g w idg g w id idTD
TD
TD
1 1 1...
and idg id idnTD
nTD
TD
1
...
So the theorem is proofed.
IV Experiment
4.1 The experiment data
The data material of this experiment is come from
and the experiment data is established as follows:
Step1: select several different several data-sets of TSP from the TSP database, and use one point represents a server node of the cloud. The data-set represents one city. Step2: each node plus a offset which far bigger than the coordinate of dataset’s node coordinate, and make sure the same dataset node having same offset.
Step3: make sure all dataset is far away from each other, or go to step2.
Step 4: set the location of center data base. The selected dataset and offset as follows:
Table1 data of experience Cloud id Dataset name Coordinate offset The TSP length 1 ei51 (0,2000) 426 2 ei51 (2000,0) 426 3 ei76 (1000,1000) 538 4 ei101 (0,500) 629 5 ei51 (2000,2000) 426 6 ei51 (500,0) 426
As table 1 shows the all city is created by 3 different data sets, and offset is far larger than TSP length.
The coordinate of the center data base is location is (1600, 1200) and (600, 700).
4.2 The experiment result
Figure 1 shows the node of city and center base location 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500
the node location of the cloud
x y city 1 city 2 city 3 city 4 city 5 city 6 center base1 center base2
Figure 1 the node location of the cloud
Figure 1 shows the node of the experiment and the two center base. The reason why the city 1ooks like one point is that inside distance of city is far smaller than the distance between the city.
Figure 2 show the improved PSO algorithm result of under situation one server node each city.
0 2 4 6 8 10 12 14 16 18 20 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4 experiment number th e d is ta n c e o f th e c o m m u n ic a ti o n
total distance of communication length between experiment round
center base1 center base2
Figure 2 Total distance of communication length between experiment round
The figure 2 shows the total communication length between round numbers. The communication length between the different experiment round is close to each other because the stability of improved PSO algorithm and the region is fit for the experiment which fits theorem 2.
Figure 3 shows the relationship between the communication number and the communication length.
1 2 3 4 5 6 7 8 9 10 0 5 10 15x 10 4
number of each city communication node
th e c o m m u n ic a tio n l e n g th
the relationship between the communication number and communication length
center base 1 center base 2
Figure 3 the relationship between the communication number and communication length
Figure 3 show the relationship between
communication node number of each city and the total communication. The figure 2 shows the communication length with the increase of the node number of each city, and it is almost like to bedirect ratio which is fits with inference2.
V conclusion
The improvement PSO algorithm is presented to handle the problem of cloud computing server points location. Though theoretical derivation, the correctness of
the algorithm. The correctness of the theoretical
derivation is verified by the experiment. Reference
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